Cellular Potts Model: Applications to Vasculogenesis and Angiogenesis

Abstract

The cellular Potts model (CPM, a.k.a. Glazier–Graner–Hogeweg or GGH model) is a somewhat liberal extension of probabilistic cellular automata. The model is derived from the Ising and Potts models and represents biological cells as domains of CA-sites of the same state. A Hamiltonian energy is used to describe the balance of forces that the biological cells apply onto one another and their local environment. A Metropolis algorithm iteratively copies the state from one site into one of the adjacent sites, thus shifting the domain interfaces and moving the biological cells along the lattice. The approach is commonly used in applications of developmental biology, where the CPM often interacts with systems of ordinary-differential equations that model the intracellular chemical kinetics and partial-differential equations that model the extracellular chemical signal dynamics to constitute a hybrid and multiscale description of the biological system. In this chapter we will introduce the cellular Potts model and discuss its use in developmental biology, focusing on the development of blood vessels, a process called vascular morphogenesis. We will start by introducing a range of models focusing on uncovering the basic mechanisms of vascular morphogenesis: network formation and sprouting and then show how these models are extended with models of intracellular regulation and with interactions with the extracellular micro-environment. We then briefly review the integration of models of vascular morphogenesis in several examples of organ development in health and disease, including development, cancer, and age-related macular degeneration. We end by discussing the computational efficiency of the CPM and the available strategies for the validation of CPM-based simulation models.